Question

multiply the following rational expressions.
\frac{2b^{2}+7b - 4}{b^{2}+b - 12}cdot\frac{b^{2}-9}{2b^{2}+5b - 3}

\frac{2b^{2}+7b - 4}{b^{2}+b - 12}cdot\frac{b^{2}-9}{2b^{2}+5b - 3}=square
(simplify your answer. use integers or fractions for any numbers in the expression.)

Explanation:

Step1: Factor the polynomials

$2b^{2}+7b - 4=(2b - 1)(b + 4)$; $b^{2}-9=(b + 3)(b - 3)$; $b^{2}+b - 12=(b + 4)(b - 3)$; $2b^{2}+5b - 3=(2b - 1)(b+3)$

Step2: Substitute the factored - forms into the original expression

$\frac{2b^{2}+7b - 4}{b^{2}+b - 12}\cdot\frac{b^{2}-9}{2b^{2}+5b - 3}=\frac{(2b - 1)(b + 4)}{(b + 4)(b - 3)}\cdot\frac{(b + 3)(b - 3)}{(2b - 1)(b + 3)}$

Step3: Cancel out the common factors

Cancel out the common factors $(2b - 1)$, $(b + 4)$, $(b - 3)$ and $(b + 3)$ in the numerator and denominator.
$\frac{(2b - 1)(b + 4)(b + 3)(b - 3)}{(b + 4)(b - 3)(2b - 1)(b + 3)} = 1$

Answer:

$1$